Foot (length)

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A foot (plural: feet or foot;^[1] symbol or abbreviation: ft or, sometimes, ′ – the prime symbol) is a non-SI unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. Its size can vary from system to system, but in each is around a quarter to a third of a meter. The most commonly used foot today is the international foot. There are three feet in a yard and 12 inches in a foot.

Contents 1 Definition 1.1 International foot 1.2 Survey foot 1.3 Pre-1959 2 Obsolete use in different countries 3 Historical origin 4 See also 5 External links 6 Notes

[edit] Definition

[edit] International foot

In 1958 the United States and countries of the Commonwealth of Nations defined the length of the international yard to be 0.9144 meters, effective July 1, 1959. Consequently, the international foot is defined to be equal to 0.3048 meters (equivalent to 304.8 millimeters). This was 2 ppm shorter than the previous U.S  definition and 1.7 ppm longer than the previous British definition.^[2]

The international standard symbol for a foot is "ft" (see ISO 31-1, Annex A). In some cases, the foot is denoted by a prime, which is often approximated by an apostrophe, and the inch by a double prime; for example, 2 feet 4 inches is sometimes denoted as 2′ 4″. This use can cause confusion, because the prime and double prime are also international standard symbols for arcminutes and arcseconds.

[edit] Survey foot

By the time the international foot was defined in 1959, there was already a huge amount of survey data which had been collected based on the former definitions, especially in the United States and in India. The small difference between survey and international feet would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when a state plane coordinate system is used, because the origin of the system may be hundreds of miles from the point of interest. Hence the previous definitions continued in use for surveying in these two countries for many years, and are denoted survey feet to distinguish them from the international foot. The United Kingdom was unaffected by this problem, as the retriangulation of Great Britain (1936–62) was done in meters.

The United States survey foot is defined as exactly ¹²⁰⁰⁄₃₉₃₇ meters, approximately 0.3048006 m.^[3] In 1986 the National Geodetic Survey (NGS) released the North American Datum of 1983, which underlies the state plane coordinate systems and is entirely defined in meters. An NGS policy from 1991 has this to say about the units used with the new datum to define the SPCS 83:

In preparation for the adjustment of the North American Datum of 1983, 31 states enacted legislation for the State Plane Coordinate System of 1983 (SPCS 83). All states defined SPCS 83 with metric parameters. Within the legislation, the U.S. Survey Foot was specified in 11 states and the International Foot was specified in 6 states. In all other states the meter is the only referenced unit of measure in the SPCS 83 legislation. The remaining 19 states do not yet have any legislation concerning SPCS 83.^[4]

Since that time, several states have abandoned the non-metric versions of SPCS 83: seven states continue to keep location data in survey feet as well as in meters, while an eighth keeps data in international feet as well as in meters.^[5] State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). Twenty-four states have legislated that surveying measures should be based on the U.S. survey foot, eight have legislated that they be made on the basis of the international foot, and eighteen have not specified the conversion factor from metric units.^[5]

The Indian survey foot is defined as exactly 0.3047996 meters,^[6] presumably derived from a measurement of the previous Indian standard of the yard. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum,^[7] which is also used by the Global Positioning System.

[edit] Pre-1959

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 by 39.37 inches = 1 meter. In Imperial units, the foot was defined as ⅓ yard, with the yard being realized as a physical standard (separate from the standard meter). The yard standards of the different Commonwealth countries were periodically compared with one another.^[8] The value of the United Kingdom primary standard of the yard was determined in terms of the meter by the National Physical Laboratory in 1964 as 0.9143969 m,^[9] implying a pre-1959 foot in the UK of 0.3047990 m.

[edit] Obsolete use in different countries

• 1 Amsterdam foot (voet) = 0.2831 m.
• 1 Danish foot (after 1835) = 0.31385 m.
• 1 French foot (pied du roi) = 12 pouces = 0.32484 m.
• 1 Norwegian foot (after 1824) = 0.31375 m.
• 1 Portuguese foot = 0.3285 m.
• 1 Rotterdam foot = 0.296 m.
• 1 Russian foot (English foot borrowed by Peter Ι) = 12 inches = 1/7 Russian sazhens = 0.3048 m.
• 1 Spanish foot (till 1752) (Pie (foot) de Ribera/de Rey) = 12 Pulgadas = 0.287342 m.
• 1 Spanish foot (1752 to 1765) (Pie (foot) de Burgos/Castellano) = 0.278635 m.
• 1 Spanish foot (after 1765) (Pie (foot) de Rey) = 12 Pulgadas = 0.32483 m.
• 1 Swedish foot (fot) = 12 inches (tum) = 0.2969 m.
• 1 Venetian foot = 0.34773 m.

[edit] Historical origin

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The foot as a unit of measure was used in most Western cultures and was usually divided into 12 or sometimes 10 inches/thumbs, or into 16 fingers/digits. The first known standard foot measure was from Sumer, where a definition is given in a statue of Gudea of Lagash from around 2575 BC. Some metrologists speculate that the imperial foot was adapted from an Egyptian measure by the Greeks, with a subsequent larger foot being adopted by the Romans.

The popular belief is that the original standard was the length of a man's foot. In rural regions and without calibrated rulers, many units of measurement were in fact based on the length of some part of body of the person measuring (or for example the area that could be ploughed in a day). In that sense, the human foot was no doubt the origin of the measuring unit called a "foot" and was also for a long time the definition of its length. To prevent discord and enable trade, many towns decided on a standard length and displayed this publicly. In order to enable simultaneous use of the different units of length based on different parts of the human body and other "natural" units of length, the different units were redefined as multiples of each other, whereby their lengths no longer corresponded to the original "natural" standards. This process of national standardization began in Scotland in 1150 and in England in 1303, but many different regional standards had existed in both these countries long before.

Some believe that the original measurement of the English foot was from King Henry I, who had a foot 12 inches long; he wished to standardize the unit of measurement in England. However this is unlikely, because there are records of the word being used approximately 70 years before his birth ^[10]. This of course does not exclude the possibility that this old standard was redefined ("calibrated") according to the ruler's foot. In fact, there is evidence that this sort of process was common before standardization. A new, important ruler could try to impose a new standard for an existing unit, but it is unlikely that any king's foot was ever as long as the modern unit of measurement.

The average foot length is about 9.4 inches (240 mm) for current Europeans. Approximately 99.6% of British men have a foot that is less than 12 inches long. One attempt to "explain" the "missing" inches is that the measure did not refer to a naked foot, but to the length of footwear, which could theoretically add an inch or two to the naked foot's length. This is consistent with the measure being convenient for practical uses such as building sites. People almost always pace out lengths while wearing shoes or boots, rather than removing them and pacing barefoot.

There are however historical records of definitions of the inch based on the width (not length) of a man's thumb that are very precise for the standards of the time. One of these was based on an average calculated using three men of different size, thereby enabling surprising accuracy and uniformity throughout a country even without calibrated rulers. It therefore seems likely that at least since about the Twelfth century, the precise length of a foot was in fact based on the inch, not the other way around. Since this length was fairly close to the size of most feet, at least in shoes, this enabled the above-mentioned use of one's shoes in approximating lengths without measuring devices. This sort of imprecise measuring that in addition excessively multiplied the measuring error due to repeated use of a short "ruler" (the foot) was never used in surveying and in constructing more complicated buildings.

[edit] See also

• anthropic units
• Units of measurement
• History of measurement
• Systems of measurement
• Weights and measures
• English unit
• Imperial unit
• United States customary units
• International System of Units
• Inch

[edit] External links

• Library of Units and Constants
• Measurements and Conversions
• Does the Foot Fit Britannia?

[edit] Notes